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Distance magic labelling of Mycielskian graphs
Electronic Journal of Graph Theory and ApplicationsA graph G = (V, E), where |V(G)| = n and |E(G)| = m is said to be a distance magic graph if there is a bijection f : V(G)→{1, 2, …, n} such that the vertex weight w(u)=∑v ∈ N(u)f(v)=k is constant and independent of u, where N(u) is an open neighborhood ...
Ravindra Kuber Pawar, Tarkeshwar Singh
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On Distance Magic Harary Graphs
, 2018 This paper establishes two techniques to construct larger distance magic and (a, d)-distance antimagic graphs using Harary graphs and provides a solution to the existence of distance magicness of legicographic product and direct product of G with C4, for every non-regular distance magic graph G with maximum degree |V(G)|-1.
Prajeesh, A V, Paramasivam, Krishnan
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Group distance magic cubic graphs
Discussiones Mathematicae Graph TheoryA $Γ$\emph{-distance magic labeling} of a graph $G = (V, E)$ with $|V| = n$ is a bijection $\ell$ from $V$ to an Abelian group $Γ$ of order $n$, for which there exists $μ\in Γ$, such that the weight $w(x) =\sum_{y\in N(x)}\ell(y)$ of every vertex $x \in V$ is equal to $μ$. In this case, the element $μ$ is called the \emph{magic constant of} $G$.
Sylwia Cichacz, Štefko Miklavič
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Distance Magic Labeling of Generalised Mycielskian Graphs
, 2023 In this paper, we have studied the distance magic labelling of Generalised Mycielskian of a few families of graphs.
Pawar, Ravindra, Singh, Tarkehswar
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Note on Group Distance Magic Graphs G[C 4] [PDF]
Graphs and Combinatorics, 2013 A \emph{group distance magic labeling} or a $\gr$-distance magic labeling of a graph $G(V,E)$ with $|V | = n$ is an injection $f$ from $V$ to an Abelian group $\gr$ of order $n$ such that the weight $w(x)=\sum_{y\in N_G(x)}f(y)$ of every vertex $x \in V$ is equal to the same element $μ\in \gr$, called the magic constant. In this paper we will show that
Sylwia Cichacz, Cichacz Sylwia
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On Structural and Spectral Properties of Distance Magic Graphs
, 2023 A graph $G=(V,E)$ is said to be distance magic if there is a bijection $f$ from a vertex set of $G$ to the first $|V(G)|$ natural numbers such that for each vertex $v$, its weight given by $\sum_{u \in N(v)}f(u)$ is constant, where $N(v)$ is an open neighborhood of a vertex $v$. In this paper, we introduce the concept of $p$-distance magic labeling and
Mukherjee, Himadri +2 more
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On the uniqueness of d-vertex magic constant
Discussiones Mathematicae Graph Theory, 2014 Let G = (V,E) be a graph of order n and let D ⊆ {0, 1, 2, 3, . . .}. For v ∈ V, let ND(v) = {u ∈ V : d(u, v) ∈ D}. The graph G is said to be D-vertex magic if there exists a bijection f : V (G) → {1, 2, . . .
Arumugam S. +2 more
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On D-distance (anti)magic labelings of shadow graph of some graphs
Electronic Journal of Graph Theory and ApplicationsLet G be a graph with vertex set V(G) and diameter diam(G). Let D ⊆ {0, 1, 2, 3, …, diam(G)} and φ : V(G)→{1, 2, 3, …, |V(G)|} be a bijection. The graph G is called D-distance magic, if s ∈ ND(t)φ(s) is a constant for any vertex t ∈ V(G). The graph G is
Anak Agung Gede Ngurah +2 more
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Self-Reverse Labelings of Distance Magic Graphs
Bulletin of the Malaysian Mathematical Sciences SocietyAbstract A graph is distance magic if it admits a bijective labeling of its vertices by integers from 1 up to the order of the graph in such a way that the sum of the labels of all the neighbors of a vertex is independent of a given vertex.
Petr Kovář, Primoz Šparl
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A Complete Characterization of Magic Constants Arising from Distance Magic Graphs
Journal of Combinatorial Mathematics and Combinatorial Computing, 2023 A positive integer \(k\) is called a magic constant if there is a graph \(G\) along with a bijective function \(f\) from \(V(G)\) to the first \(|V(G)|\) natural numbers such that the weight of the vertex \(w(v) = \sum_{uv \in E} f(u) = k\) for all \(v \in V\).
Pawar, Ravindra +3 more
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